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Section 5.3 GRAPH CONCEPTS AND TERMINOLOGY

Section 5.3 GRAPH CONCEPTS AND TERMINOLOGY. 1) Degree of a vertex - the number of edges at the vertex a) a loop counts twice b) odd vertex - a vertex of odd degree c) even vertex - a vertex of even degree. List all of the odd vertices: __________________

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Section 5.3 GRAPH CONCEPTS AND TERMINOLOGY

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  1. Section 5.3 GRAPH CONCEPTS AND TERMINOLOGY

  2. 1) Degree of a vertex - the number of edges at the vertexa) a loop counts twiceb) odd vertex - a vertex of odd degreec) even vertex - a vertex of even degree List all of the odd vertices: __________________ List even vertices: _____________________

  3. 2) Adjacent vertices - two vertices are adjacent if there is an edge joining them3) Adjacent edges - two edges are adjacent if they share a common vertex List a pair of adjacent vertices: __________ List a pair of adjacent edges: ___________

  4. 4) Path - a sequence of vertices such that each vertex in the sequence is adjacent to the next one and no edge appears in the path more than once. *** The number of edges in a path is called the length of the path. Each edge has a length of 1; a loop has length of 1 List a path of length 5 from A to G: ___________________ List a path of length 7 from A to G: ___________________

  5. 5) Circuit - a path which starts and ends at the same vertex (multiple edges and loops are circuits). List 2 circuits and give their length _______________ _______________

  6. 6) Connected graph - a graph for which any two of its vertices can be joined by a path7) Disconnected graph - a graph made up of connected pieces

  7. 8) Euler path - a path which travels through every edge of a graph A B E C D Example: An Euler path: D, E, A, B, E, C, B, D, C

  8. 9) Euler circuit - a circuit which travels through every edge of a graph A E Example: An Euler circuit: D, E, A, B, E, C, B, D, C, F, D B D C F

  9. 10) Bridge - an edge, which if removed, disconnects the graph Is there a bridge? If yes, which one? _______________

  10. Draw a graph with 3 vertices, each of degree 2 • Draw a connected graph with 3 vertices, each of degree 4

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